CAT 2025 Slot 1 · DILR · Set 2: InnovateX — Elite and Novice Ratings

Each quarter sends exactly one person down from Elite and one up from Novice.

Clue 1 requires all three starters in Elite to end up in Novice by Quarter 4, which takes three demotions in three quarters — so one of Asha, Bunty and Chintu goes down each quarter and nobody returns.

Clue 3 has Lalu rating Bunty in Quarter 2, so Bunty was already in Novice then and was demoted at the end of Quarter 1.

Clue 3 also has Lalu rating Asha in Quarter 3, so Asha was demoted at the end of Quarter 2, leaving Chintu to go at the end of Quarter 3.

Dolly is still with Lalu in Quarter 3, so she is the one promoted at the end of Quarter 3, and her Quarter 3 rating of 2 plus clue 2 makes her rating 2 in every quarter.

In Quarter 1 the Novice trio is Dolly, Eklavya and Falguni with distinct ratings, and Dolly takes the 2, so Eklavya and Falguni hold 1 and 3.

The one rated 3 has the highest score and is promoted at the end of Quarter 1.

Suppose Eklavya took the 3. Then Eklavya moves up and Falguni, rated 1, must keep rating 1 in Quarter 2 by clue 2 — but Bunty is also rated 1 in Quarter 2 and both are in Novice, which breaks the distinct-ratings rule.

So Falguni took the 3 in Quarter 1 and holds 3 throughout, while Eklavya took the 1.

In Quarter 2 the Novice trio is Bunty, Dolly and Eklavya, with Bunty on 1 and Dolly on 2, so Eklavya is rated 3.

Eklavya's score at the end of Quarter 2 is 1+3=4.

Shortcut. Clue 2 is the lever: whoever is promoted first must leave a partner behind whose fixed rating would clash with Bunty's 1 in Quarter 2. That single clash settles Eklavya's Quarter 1 rating without building the full table.

Exactly one promotion and one demotion happen at the end of each quarter, so three quarters produce three of each.

Clue 1 says Asha, Bunty and Chintu all begin in Elite and are all in Novice by Quarter 4.

Three demotions are available and three people must each be demoted at least once, so each of them is demoted exactly once and never comes back.

The three promotions therefore all go to Dolly, Eklavya and Falguni, one each.

Every one of the six employees thus changes group exactly once.

So no employee changed groups more than once, and the answer is 0.

Shortcut. Counting the moves settles it without any ratings: three quarters give three demotions, and three named people must each use one. There is nothing left over for a second move by anybody.

Bunty starts in Elite and is demoted at the end of Quarter 1, so his Quarter 1 rating came from Kuku.

A demotion goes to the Elite member with the lowest score, and after one quarter the score is just that quarter's rating.

Since the three Elite ratings are 1, 2 and 3, Bunty's Quarter 1 rating was 1.

Clue 3 gives his Quarter 2 rating as 1, awarded by Lalu in Novice.

In Quarter 3 the Novice trio is Asha, Bunty and Dolly, rated distinctly from 1 to 3.

Clue 3 fixes Asha at 1 and Dolly at 2, so Bunty takes the remaining 3.

His score is therefore 1+1+3=5.

Shortcut. Bunty's three ratings are each forced by a different mechanism — the demotion rule, a direct clue, and the leftover of a distinct triple. None of them needs the rest of the table.

Four of the six scores are forced outright.

Bunty is rated 1, 1 and 3 across the three quarters, giving 5.

Dolly holds rating 2 in every quarter, giving 6.

Falguni holds rating 3 in every quarter, giving 9.

Eklavya is rated 1 in Quarter 1 and 3 in Quarter 2; in Quarter 3 the Elite trio is Chintu, Eklavya and Falguni, and Falguni's fixed 3 leaves 1 and 2 for the other two.

Chintu must be demoted at the end of Quarter 3, so he needs the lower score, which requires Chintu to take the 1 and Eklavya the 2 — giving Eklavya 1+3+2=6.

Asha and Chintu are the two that stay open.

In Quarter 1 Bunty takes the rating 1, so Asha and Chintu share 2 and 3; in Quarter 2 Falguni takes 3, so Asha and Chintu share 1 and 2.

Asha must be demoted at the end of Quarter 2, and checking the possibilities leaves two consistent arrangements: Asha 2 then 1 with Chintu 3 then 2, or Asha 3 then 1 with Chintu 2 then 2.

Those give Asha a Quarter 3 score of 4 or 5, and Chintu 6 or 5, so neither is certain.

The count of employees with a determinable score is therefore 4.

Shortcut. Everyone whose ratings are fixed by a constant or by a leftover is certain; only the pair who share two unordered pairs of ratings stays open. Spotting that Asha and Chintu are that pair answers the question without evaluating either branch.

In Quarter 1 the Elite trio is Asha, Bunty and Chintu, and Bunty's demotion forces his rating to 1.

That leaves ratings 2 and 3 for Asha and Chintu, in either order for now.

In Quarter 2 the Elite trio is Asha, Chintu and Falguni, and Falguni's fixed rating is 3.

So Asha and Chintu share the ratings 1 and 2 in Quarter 2.

Asha must be demoted at the end of Quarter 2, so her two-quarter score must be the lowest in Elite.

Falguni's score is 3+3=6, comfortably above either candidate, so the contest is between Asha and Chintu.

If Asha takes the 2 in Quarter 2 then Chintu takes the 1, and Asha's score beats or ties Chintu's with a higher latest rating — so Chintu would go down instead.

Hence Asha must take the rating 1 in Quarter 2, making statement II necessarily true.

For Quarter 1 both splits survive: Asha 2 with Chintu 3 gives scores 3 and 5, and Asha 3 with Chintu 2 gives 4 and 4 with Asha ranked lower on the latest rating — Asha is demoted either way.

So statement I is not necessarily true, and the answer is "Only II", the fourth option.

Shortcut. The demotion rule bites in Quarter 2 but not in Quarter 1, because the tie-break rescues the second arrangement there. Checking which quarter the rule actually constrains answers the question in one pass.